Topic Archive: uplifting cardinals
The City University of New York
Professor Hamkins (Ph.D. 1994 UC Berkeley) conducts research in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite. He has been particularly interested in the interaction of forcing and large cardinals, two central themes of contemporary set-theoretic research. He has worked in the theory of infinitary computability, introducing (with A. Lewis and J. Kidder) the theory of infinite time Turing machines, as well as in the theory of infinitary utilitarianism and, more recently, infinite chess. His work on the automorphism tower problem lies at the intersection of group theory and set theory. Recently, he has been preoccupied with various mathematical and philosophical issues surrounding the set-theoretic multiverse, engaging with the emerging debate on pluralism in the philosophy of set theory, as well as the mathematical questions to which they lead, such as in his work on the modal logic of forcing and set-theoretic geology.
BerkeleyCSICUNYCaltechGraduate CenterJapanNew YorkUvAapproximation and coverautomorphism towercomputabilityforcinginfinitary computabilityinfinite chesslarge cardinalsmaximality principlemultiversephilosophical logicphilosophyphilosophy of mathematicsphilosophy of set theoryset theoryset-theoretic geologytall cardinalsunfoldable cardinalsuplifting cardinals